4o-aquarium

gistfile1.txt

<USER>
### 2. Aquarium

In the aquarium, there are octopuses with eight arms and starfish with five arms.

**How many starfish are there in the aquarium if the total number of arms of all the animals living in it is 41?**

<ASSISTANT>
Let's solve this step by step.

### Step 1: Define Variables
- Let **x** = number of octopuses
- Let **y** = number of starfish

### Step 2: Set Up the Equation
Each octopus has 8 arms, and each starfish has 5 arms. The total number of arms is 41. So, the equation becomes:

\[
8x + 5y = 41
\]

### Step 3: Find Integer Solutions
Since the number of animals can't be negative or fractional, we look for **non-negative integer solutions**.

We'll test different values of **x**:

- **If \( x = 0 \):** \( 5y = 41 \) → \( y = 8.2 \) (not an integer)
- **If \( x = 1 \):** \( 8 + 5y = 41 \) → \( 5y = 33 \) → \( y = 6.6 \) (not an integer)
- **If \( x = 2 \):** \( 16 + 5y = 41 \) → \( 5y = 25 \) → \( y = 5 \) ✅ (integer solution)
- **If \( x = 3 \):** \( 24 + 5y = 41 \) → \( 5y = 17 \) → \( y = 3.4 \) (not an integer)
- **If \( x = 4 \):** \( 32 + 5y = 41 \) → \( 5y = 9 \) → \( y = 1.8 \) (not an integer)
- **If \( x = 5 \):** \( 40 + 5y = 41 \) → \( 5y = 1 \) → \( y = 0.2 \) (not an integer)

No other positive integer solutions exist.

### ✅ Final Answer:
The aquarium has **5 starfish**.